Mary is trying to stop a 5 kg bowling ball that is rolling toward her. Its horiz
ID: 1530778 • Letter: M
Question
Mary is trying to stop a 5 kg bowling ball that is rolling toward her. Its horizontal velocity is 8.0
m/s when she begins to stop it. It takes her 2.0 s to stop the ball. What average force did Mary
exert on the ball during this 2.0 s to stop it? Assume that the bowling ball is rolling on a flat, horizontal surface. Also, unless it is stated
otherwise, assume that there is no friction acting on the bowling ball.
1.) This problem can be solved in two different ways using two different pairs of
equations. List the two equations that would be used for each solution method, in the
order in which they would be used in solving the problem.
· First solution method: 1st equation: ____ 2nd equation: ____
· Second solution method: 1st equation: ____ 2nd equation: ____
2.) Other factors noted in the problem being equal, which of the following changes
would increase the magnitude of the average force that Mary needs to exert on the ball to
stop it? Note: You will need to convert from weight in lb. to mass in kg in (a).
a. ___ T ___ F: It is a 10 lb. bowling ball
b. ___ T ___ F: The horizontal velocity of the ball is 9 m/s when she begins to stop it
c. ___ T ___ F: It takes her 1.5 s to stop the ball
d. ___ T ___ F: Mary applies her force higher on the ball, causing 4 N of friction to act
on the ball, opposite to the direction in which it is traveling
Explanation / Answer
One method to find solution is using the equation:
F = m × a
where m is mass of the bowling ball = 5 kg
acceleration a = v / t
v = change in velocity= Vf - Vi = (0 m/s) - (8 m/s) = -8 m/s
Vi = initial velocity = 8 m/s
Vf = final velocity = 0 m/s
t = time taken to stop the ball = 2 s
The average force exerted on the ball to stop it is:
F = m × v / t
F = (5 kg) × (-8 m/s) / 2
F = -20 N
The negative sign just indicates that the direction of the force is opposite to the direction of the ball.
Second method to find solution is using the equation:
Work done W = Fnet × x ------------(1)
Fnet = (Work done W) / x
where x is the distance travelled by the ball before coming to hault.
Work done by the net force = change in kinetic energy (KE)
So Fnet = (KE) / x ------------(2)
KE = ½(m Vf2) - ½(m Vi2)
Vi = initial velocity = 8 m/s
Vf = final velocity = 0 m/s
m is mass of the bowling ball = 5 kg
KE = ½ m (Vf2 - Vi2) = ½ ×5 (64-0) =160 N m
x = ½ (Vi + Vf) t
x = ½ × 8 × 2 = 8 m
Substituting KE and x in equation (2)
Fnet = (160 N m) / 8 m
Fnet = 20 N, force is exerted in the opposite direction
Fnet = -20 N
(2) Mary applies her force higher on the ball, causing 4 N of friction to act on the ball, opposite to the direction in which it is travelling.